To the theory of dimensional quantization in crystals in the Kane approximation

Abstract

The microscopic mechanism of size quantization of the conduction band and valence band of semiconductors of cubic and tetrahedral symmetry has been theoretically studied in the Kane approximation. It is shown that the matrix Schrödinger equation obtained on the basis of the Kane model cannot be solved analytically for a potential well of an arbitrary profile. Therefore, expressions for the energy spectrum are obtained depending on the two-dimensional wave vector directed along the interface of the heterostructure for various cases that differ in the range of current carrier energy values.